1. Field of the Invention
This invention relates in general to the field of electronic circuit devices, and more particularly to an apparatus and method for digitally synthesizing variable frequency sinusoidal waveforms.
2. Description of the Related Art
In electronic systems, in particular those which are used in the communications field, the requirement to generate sinusoidal waveforms of varying frequency is very prevalent. Elementary physics tells us that the most effective and efficient means of transmitting information over long distancesxe2x80x94regardless of whether the medium of transmission is wire, air, water, or some other substancexe2x80x94is to encode the information for transmission such that it is represented in the form of a sinusoid.
Virtually every electronic communications product on the market today employs multiple circuits whose only function is to generate a sinusoidal waveform at a prescribed frequency. Radios require such circuits so that they can receive a transmission over a specific channel. Telephones utilize specified frequency tones to indicate dialing sequences. And wireless products such as cellular telephones and pagers modulate voice signals for transmission over narrow and constantly changing frequency bands using sinusoidal modulation components. Spread-spectrum portable telephones utilize sinusoidal components to modulate voice at rapidly changing frequencies between a base station and a hand-held receiver. The list goes on and on.
In fact, certain products, specifically portable phones, cell phones, and pagers, could never have been developed using early apparatus to synthesize variable frequency sinusoidal waveforms. These early frequency synthesizers consisted entirely of analog electronic components that were heavy, complex, costly, and required lots of power to operate. Moreover, once set to a prescribed frequency, they typically had to be periodically reset because they tended to drift in frequency when operating temperature changed or as a function of operating time.
But all this changed with the introduction of digital frequency synthesis techniques. Because of the precision, speed, and low power requirement of digital logic devices, digital frequency synthesizers can be produced that are precise, small, inexpensive, and that can be operated in conjunction with other circuits for acceptable time periods on battery power alone. The proliferation of cell phones and pagers in our present culture attests to the enabling features of digital frequency synthesis techniques.
A present day digital frequency synthesizer consists of a phase signal generator and a phase-to-amplitude converter. The phase signal generator is loaded with a value that corresponds to a desired sinusoidal output frequency. Then, in synchronization with a clock signal, the phase signal generator produces digital data words at the frequency of the clock signal that correspond to phase samples ranging between 0 degrees and 360 degrees of the desired output signal. For example, at a clock signal rate of 100 MHz, if the phase signal generator produces phase samples that are 36 degrees apart (i.e., 0xc2x0, 36xc2x0, 72xc2x0, etc.), then this sequence corresponds to a 10 MHz output frequency.
This synthesized phase signal is then converted to an output amplitude by the phase-to-amplitude converter. Typically, a number of amplitude samples, each corresponding to a specific phase angle value for the output sinusoid are stored in a memory device such as a read-only memory (ROM) within the phase-to-amplitude converter. The phase signal is used to address a specific amplitude sample, which is then provided in digital form to an analog-to-digital converter. The analog to digital converter then produces a continuous amplitude waveform, changing the amplitude magnitude with each cycle of the clock signal.
From the above discussion, one skilled in the art can deduce that the generation of low-distortion sinusoids demands that a large number of amplitude samples be available for output within the ROM. Yet the storage of many samples requires many storage locations, proportionately increasing the cost, complexity, and power requirements of the digital frequency synthesizer. Fortunately, several techniques have been developed in more recent years that exploit the quadrature symmetry of sinusoidal waveforms so that storage location requirements are decreased by 75 percent. In addition, other compression techniques have been provided that allow even further reductions in power and size. One such technique utilizes Taylor Series expansion terms to improve the resolution of an amplitude sample corresponding to an intermediate phase angle, that is, an angle that is in between two angle values mapped by the ROM. But one skilled in the art will appreciate that for generation of a sine wave, to employ a meaningful Taylor series approximation, a term corresponding to a cosine wave must also be generated. Taylor series techniques are effective, but they require that both sine and cosine amplitudes be generated.
In spite of the advantages afforded by present day digital frequency synthesis techniques, application demands for mobile, portable, hand-held, and battery operated products continue to force designers to seek synthesizers that are less complex, that are more reliable, that are more precise, that use less power, and hence, that are less costly.
Therefore, what is needed is a digital frequency synthesizer that further exploits the symmetries inherent in sinusoidal waveforms to achieve further amplitude storage compression.
In addition, what is needed is an apparatus for simultaneously synthesizing sine and cosine wave components that only requires generation of amplitudes corresponding to an octant ranging in phase from 0 to 45 degrees for each of the components.
Furthermore what is needed is an octant-based digital frequency synthesizer for providing spectrally pure sine and cosine wave outputs.
Moreover, what is needed is a method for producing a sinusoidal waveform that uses only sine and cosine amplitude samples corresponding to an octant ranging from 0 degrees to 45 degrees in phase.
To address the above-detailed deficiencies, it is an object of the present invention to provide a digital frequency synthesizer that is based upon octant symmetries observed in a sine wave and cosine wave, taken together.
Accordingly, in the attainment of the aforementioned object, it is a feature of the present invention to provide a frequency synthesizer for producing a sinusoidal waveform. The frequency synthesizer includes a phase signal and a phase-to-amplitude converter. The phase signal indicates a desired phase angle of the sinusoidal waveform. The phase-to-amplitude converter is coupled to the phase signal. The phase-to-amplitude converter provides a desired amplitude sample corresponding to the desired phase angle, where the desired amplitude sample is derived from amplitude samples corresponding to an octant of the sinusoidal waveform The phase-to-amplitude converter includes a Haar Transform-based coarse octant amplitude sample generator that computes Haar coefficients corresponding to the phase signal and transforms the Haar coefficients into the desired amplitude sample.
An advantage of the present invention is that it requires less power to operate than that which has heretofore been provided.
Another object of the present invention is to provide an apparatus for simultaneously synthesizing sine and cosine wave components that translates of sine and cosine amplitudes corresponding an octant ranging in phase from 0 to 45 degrees to an octant corresponding to a desired phase angle.
In another aspect, it is a feature of the present invention to provide a digital frequency synthesizer for simultaneously producing a sine wave and a cosine wave, the sine wave and the cosine wave being at a prescribed frequency. The digital frequency synthesizer has an amplitude sample generator, a symmetry controller, and interpolation logic. The amplitude sample generator computes Haar coefficients corresponding to a desired phase angle, and transforms the Haar coefficients into a particular in-phase amplitude sample and a particular quadrature amplitude sample. The amplitude sample generator also generates amplitude samples that lie within a first phase octant ranging from 0 degrees to 45 degrees. The amplitude sample generator has in-phase amplitude samples, for indicating sine wave amplitudes within the first phase octant, and quadrature amplitude samples, for indicating cosine wave amplitudes within the first phase octant. The symmetry controller is coupled to the amplitude sample generator. The symmetry controller receives a phase signal from a phase accumulator. The phase signal indicates the desired phase angle. The symmetry controller selects the particular in-phase amplitude sample and the particular quadrature amplitude sample to provide a desired sine wave amplitude and a desired cosine wave amplitude at the desired phase angle. The interpolation logic is coupled to the symmetry controller. The interpolation logic adds a first first-order Taylor series term to the particular in-phase amplitude sample, thereby increasing precision of the sine wave. The interpolation logic includes a multiplier that multiplies fine phase bits of the phase signal by a 90 degree term to account for digital scaling difference between amplitude magnitude representations and phase magnitude representations within the frequency synthesizer.
Another advantage of the present invention is that the present invention possesses the inherent capacity to support more advanced quadrature modulation schemes.
A further object of the present invention is to provide an octant-based digital frequency synthesizer for providing spectrally pure sine and cosine wave outputs.
In a further aspect, it is a feature of the present invention to provide a computer program product for use in designing, simulating, fabricating, or testing a direct digital frequency synthesizer circuit. The computer program product includes a storage medium that has computer readable instructions embodied thereon, for causing a computer upon which the computer readable instructions are executed to describe the digital frequency synthesizer circuit such that it can be modified, simulated, fabricated, or tested. The computer readable instructions include first instructions and second instructions. The first instructions cause the computer to describe a phase signal, for indicating a desired phase angle of a sinusoidal waveform. The second instructions cause the computer to describe a phase-to-amplitude converter, coupled to the phase signal, for providing a desired amplitude sample corresponding to the desired phase angle, where the desired amplitude sample is derived from amplitude samples corresponding to an octant of the sinusoidal waveform. The phase-to-amplitude converter has a Haar Transform-based coarse octant amplitude sample generator that computes Haar coefficients corresponding to the phase signal, and that transforms the Haar coefficients into the desired amplitude sample.
A further advantage of the present invention is that it allows battery operated products to operate longer.
Yet another object of the present invention is to provide a method for producing a sinusoidal waveform that uses only amplitude samples corresponding to an octant ranging from 0 degrees to 45 degrees in phase.
In yet another aspect, it is a feature of the present invention is to provide a method for generating a sine wave and a cosine wave at a prescribed frequency by direct digital frequency synthesis. The method includes providing a phase angle signal, wherein the rate of change of the phase angle signal corresponds to the prescribed frequency; generating Haar coefficients that correspond to a first octant of the sine wave and the cosine wave; selecting specific Haar coefficients that correspond to a specific phase offset within the first octant, wherein a desired phase angle for the sine wave and the cosine wave is determined by summing a true octant base angle with the specific phase offset; and translating the specific Haar coefficients into a cosine amplitude sample and a sine amplitude sample that correspond to the desired phase angle.
Yet another advantage of the present invention is that Taylor Series techniques can easily be employed to reduce output distortion because the generation of sample components required for Taylor Series terms are provided for within an octant-based amplitude sample generator.